CAPS 2020 Problem 6

Let $ABC$ be an acute triangle. Let $P$ be a point such that $PB$ and $PC$ are tangent to circumcircle of $ABC$ . Let $X$ and $Y$ be variable points on $AB$ and $AC$ , respectively, such that $\angle XPY = 2\angle BAC$ and $P$ lies in the interior of triangle $AXY$ . Let $Z$ be the reflection of $A$ across $XY$ . Prove that the circumcircle of $XYZ$ passes through a fixed point.

(Dominik Burek, Poland)